French officials have strongly condemned anti-Semitic abuse and anti-police attacks by some gilets jaunes (yellow vests) protesters as hundreds gathered in central Paris to mark the third month of the anti-government protests.

Prosecutors have launched an investigation into a group of protesters who shouted anti-Semitic insults at philosopher and writer Alain Finkielkraut during demonstrations in the capital on Saturday.

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In a separate incident, a police car stuck in a traffic jam in Lyon, southeastern France, was stoned by demonstrators.

President Emmanuel Macron condemned the abuse directed at Finkielkraut, tweeting: “The anti-Semitic insults he has been subjected to are the absolute negation of what we are and what makes us a great nation. We will not tolerate it.”

“The son of Polish immigrants who became a French academician […] is not only a prominent man of letters but the symbol of what the Republic allows everyone,” the president added in another tweet.

The abuse - including protesters shouting “Dirty Zionist” and “France is ours” - was caught on video and broadcast on television and social media.

The stoning incident in Lyon was also captured on video, with footage filmed from inside the police car showing dozens of protesters throwing stones at the vehicle.

“We’re under attack and being stoned,” reported a policeman.

The interior minister, Christophe Castaner, described the actions of the protesters as “intolerable”.

Finkielkraut, who had voiced support for the “yellow vest” movement before later criticising it, denounced the protests as “grotesque”

“I no longer back these demonstrations, it’s becoming grotesque, it’s a movement that no longer knows how to stop,” he said.

The incident has rekindled claims by Macron that recent acts of anti-Semitic vandalism, including the painting of Nazi swastikas over portraits of famed French holocaust survivor Simone Veil, was the work of far-left and far-right activists within the gilets jaunes movement.

The vandalism came amid reports of rising anti-Jewish offences - up 74 percent last year according to police - which have caused alarm.

Fourteen political parties have called on people to demonstrate on Tuesday against anti-Semitism.

The gilets jaunes protests, which have no organised leadership, began three months ago on 17 November over increasing fuel taxes.

They quickly grew into a broader anti-government rebellion fuelled by anger towards Macron.

Some 41,500 people took the streets on Saturday, according to police, the 14th consecutive Saturday of protests across the country.

There were clashes and arrests in several cities but the level of violence and number of demonstrators were down on the previous weekend.

On Sunday, hundreds of protesters marched on the famous Champs-Elysees avenue, this time to mark the anniversary of the start of the movement.